adds tutorial

Author: ValentinKaisermayer

docs/pages.jl

@@ -4,6 +4,7 @@ pages = [
         "RC Circuit" => "tutorials/rc_circuit.md",
         "Custom Components" => "tutorials/custom_component.md",
         "Thermal Conduction Model" => "tutorials/thermal_model.md",
+        "DC Motor with Speed Controller" => "tutorials/dc_motor_pi.md",
     ],
     "API" => [
         "Basic Blocks" => "API/blocks.md",

docs/src/index.md

@@ -17,6 +17,7 @@ import Pkg; Pkg.add("ModelingToolkitStandardLibrary")
 - [RC Circuit](http://mtkstdlib.sciml.ai/dev/tutorials/rc_circuit/)
 - [Custom Component](http://mtkstdlib.sciml.ai/dev/tutorials/custom_component/)
 - [Thermal Model](http://mtkstdlib.sciml.ai/dev/tutorials/thermal_model/)
+- [DC Motor with PI-controller](http://mtkstdlib.sciml.ai/dev/tutorials/dc_motor_pi/)
 
 ## Libraries
 

docs/src/tutorials/dc_motor_pi.md

@@ -0,0 +1,93 @@
+# DC Motor with PI-controller
+In this example a PI-controller is setup for speed control of a DC-motor. First the needed packages 
+are imported and the parameters of the model defined.
+
+```@example dc_motor_pi
+using ModelingToolkit
+using ModelingToolkitStandardLibrary.Electrical
+using ModelingToolkitStandardLibrary.Mechanical.Rotational
+using ModelingToolkitStandardLibrary.Blocks
+using OrdinaryDiffEq
+using Plots
+
+@parameters t
+
+R = 0.5 # [Ohm]
+L = 4.5e-3 # [H]
+k = 0.5 # [N.m/A]
+J = 0.02 # [kg.m²]
+f = 0.01 # [N.m.s/rad]
+tau_L_step = -3 # [N.m]
+nothing # hide
+```
+
+The actual model can now be composed.
+
+```@example dc_motor_pi
+@named ground = Ground()
+@named source = Voltage()
+@named ref = Blocks.Step(height = 1, start_time = 0)
+@named pi_controller = Blocks.LimPI(k = 1.1, T = 0.035, u_max = 0.6, Ta = 0.035)
+@named feedback = Blocks.Feedback()
+@named R1 = Resistor(R = R)
+@named L1 = Inductor(L = L)
+@named emf = EMF(k = k)
+@named fixed = Fixed()
+@named load = Torque(use_support = false)
+@named load_step = Blocks.Step(height = tau_L_step, start_time = 3)
+@named inertia = Inertia(J = J)
+@named friction = Damper(d = f)
+@named speed_sensor = SpeedSensor()
+
+connections = [connect(fixed.flange, emf.support, friction.flange_b)
+               connect(emf.flange, friction.flange_a, inertia.flange_a)
+               connect(inertia.flange_b, load.flange)
+               connect(inertia.flange_b, speed_sensor.flange_a)
+               connect(load_step.output, load.tau)
+               connect(ref.output, feedback.input1)
+               connect(speed_sensor.w_rel, feedback.input2)
+               connect(feedback.output, pi_controller.err_input)
+               connect(pi_controller.ctr_output, source.input)
+               connect(source.p, R1.p)
+               connect(R1.n, L1.p)
+               connect(L1.n, emf.p)
+               connect(emf.n, source.n, ground.g)]
+
+@named model = ODESystem(connections, t,
+                         systems = [
+                             ground,
+                             ref,
+                             pi_controller,
+                             feedback,
+                             source,
+                             R1,
+                             L1,
+                             emf,
+                             fixed,
+                             load,
+                             load_step,
+                             inertia,
+                             friction,
+                             speed_sensor,
+                         ])
+nothing # hide
+```
+
+Now the model can be simulated. Typical rotational mechanical systems are described via `DAE` 
+(differential algebraic equations), however in this case ModelingToolkit can simplify the model enough
+so that it can be represented as a system of `ODEs` (ordinary differential equations).
+
+```@example dc_motor_pi
+sys = structural_simplify(model)
+prob = ODEProblem(sys, [], (0, 6.0))
+sol = solve(prob, Rodas4())
+
+p1 = Plots.plot(sol.t, sol[inertia.w], ylabel = "Angular Vel. in rad/s",
+                label = "Measurement", title = "DC Motor with Speed Controller")
+Plots.plot!(sol.t, sol[ref.output.u], label = "Reference")
+p2 = Plots.plot(sol.t, sol[load.tau.u], ylabel = "Disturbance in Nm", label = "")
+Plots.plot(p1, p2, layout = (2, 1))
+nothing # hide
+```
+
+![DC Motor with speed controller](dc_motor_pi.png)

src/Electrical/Electrical.jl

@@ -16,7 +16,8 @@ D = Differential(t)
 export Pin, OnePort
 include("utils.jl")
 
-export Capacitor, Ground, Inductor, Resistor, Conductor, Short, IdealOpAmp, EMF, HeatingResistor
+export Capacitor, Ground, Inductor, Resistor, Conductor, Short, IdealOpAmp, EMF,
+       HeatingResistor
 include("Analog/ideal_components.jl")
 
 export CurrentSensor, PotentialSensor, VoltageSensor, PowerSensor, MultiSensor